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\documentclass{article} | ||
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\usepackage{url} | ||
\usepackage{xcolor} | ||
\usepackage{tikz} | ||
\usepackage{mdframed} | ||
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\definecolor{bg}{HTML}{7681a9} | ||
\pagecolor{bg} | ||
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\usepackage[T1]{fontenc} | ||
\usepackage{newpxtext} | ||
\usepackage[vvarbb,cmintegrals,cmbraces,bigdelims]{newpxmath} | ||
\usepackage[scr=rsfso]{mathalfa}% \mathscr is fancier than \mathcal | ||
\linespread{1.04} % adds more leading (space between lines) | ||
% quantifiers look strange, so change those back to normal: | ||
\DeclareSymbolFont{mysymbols}{OMS}{cmsy}{b}{n} %note we make the figures bold to better match newpx. Replace the ``b'' with an ``m'' to undo this. | ||
%\SetSymbolFont{mysymbols} {bold}{OMS}{cmsy}{b}{n} | ||
%\DeclareSymbolFont{myoperators} {OT1}{cmr} {m}{n} | ||
%\SetSymbolFont{myoperators}{bold}{OT1}{cmr} {bx}{n} | ||
\DeclareMathSymbol{\forall}{\mathord}{mysymbols}{"38} | ||
\DeclareMathSymbol{\exists}{\mathord}{mysymbols}{"39} | ||
%\DeclareMathSymbol{\pm}{\mathbin}{mysymbols}{"06} | ||
%\DeclareMathSymbol{+}{\mathbin}{myoperators}{"2B} | ||
%\DeclareMathSymbol{-}{\mathbin}{mysymbols}{"00} | ||
%\DeclareMathSymbol{=}{\mathrel}{myoperators}{"3D} | ||
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\begin{document} | ||
\pagestyle{empty} | ||
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\begin{center} | ||
\begin{tikzpicture}[remember picture, overlay, color=bg!90!black] | ||
\def\r{.55} | ||
\newcommand{\hexbox}[3]{ | ||
\def\x{-cos{30}*\r*#1+cos{30}*#2*\r*2} | ||
\def\y{-\r*#1-sin{30}*\r*#1} | ||
\draw (\x,\y) +(90:\r) -- +(30:\r) -- +(-30:\r) -- +(-90:\r) -- +(-150:\r) -- +(150:\r) -- cycle; | ||
\draw (\x,\y) node{#3}; | ||
} | ||
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% Pascal's triangle | ||
%put row of 1's down left side: | ||
\foreach \row in {0,...,16} { | ||
\hexbox{\row}{0}{\large 1} | ||
} | ||
%fill in the rest of the triangle: | ||
\foreach \row in {1,...,16} { | ||
\pgfmathsetmacro{\entry}{1}; | ||
\foreach \col in {1,...,\row} { | ||
% iterative formula : val = precval * (row-col+1)/col | ||
% (+ 0.5 to bypass rounding errors) | ||
\pgfmathtruncatemacro{\entry}{\entry*((\row-\col+1)/\col)+0.5}; | ||
\global\let\entry=\entry | ||
\ifnum \entry<100 | ||
\hexbox{\row}{\col}{\large \entry} | ||
\else \ifnum \entry<1000 | ||
\hexbox{\row}{\col}{\entry} | ||
\else \ifnum \entry<10000 | ||
\hexbox{\row}{\col}{\footnotesize \entry} | ||
\else | ||
\hexbox{\row}{\col}{\scriptsize \entry} | ||
\fi | ||
\fi | ||
\fi | ||
} | ||
} | ||
\end{tikzpicture} | ||
\end{center} | ||
~ | ||
\vskip 5em | ||
\noindent This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Norther Colorado. This course serves both as an introduction to topics in discrete math and as the ``introduction to proof'' course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. | ||
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\vskip 2em | ||
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\noindent Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. | ||
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\vskip 2em | ||
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\noindent While there are many fine discrete math textbooks available, this text has the following advantages: | ||
\begin{itemize} | ||
\item[--] It is written to be used in an inquiry rich course. | ||
\item[--] It is written to be used in a course for future math teachers. | ||
\item[--] It is open source, with low cost print editions and free electronic editions. | ||
\end{itemize} | ||
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\vskip 7em | ||
\noindent To download the current version, or for information on obtaining the \LaTeX\ source, visit: \url{http://discretetext.oscarlevin.com/}. | ||
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\clearpage | ||
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\end{document} |
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\thispagestyle{empty} | ||
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~ | ||
\vskip 2in | ||
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\begin{flushright} | ||
\emph{\large To Shannon and Madeline} | ||
\end{flushright} | ||
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\cleardoublepage |
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